A student wants to know how to unambiguously interpret strings of trigonometric
functions, multiplication, and exponentiation. Doctor Peterson digs into a history book
-- as well as another math doctor's conversation -- to illuminate the vagaries of the
notation.

My teacher gave us ten questions to answer and I could do all except two:
1) A framed rectangular picture is 35cm long and 25cm wide... 2) The base
of a triangle is 9cm more than the perpendicular height...

A remainder of 9 results when the polynomial p(x) is divided by x-2, a
remainder of -3 when p(x) is divided by x+2, and a remainder of 3 when
divided by x-1. Find the remainder when p(x) is divided by (x-2)(x+2)(x-
1).